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The variational principles are very useful analytical tool for the study of the ground state energy of any dynamical system. In this work, we have evaluated the method and techniques of variational principle to derive the ground state energy for the harmonic, cut-off and anharmonic oscillators with a ground state wave function for a one-body Hamiltonian in three dimensions.

In this paper Dirac equation was studied in the presence of the modified Mobius square potential with a Yukawa-like tensor interaction. The eigenvalues and corresponding eigenfunctions were obtained for any-state by using Nikiforov-Uvarov method.

We solve approximately the bound state solutions of the Klein -Gordon equation for deformed Hulthen potential with unequal scalar and vector potential for arbitrary  l state. We obtain explicitly the energy eigenvalues and the corresponding wave function expressed in terms of the Jacobi polynomials. We also discuss the energy eigenvalues of our result for three cases with equal and unequal scalar and vector potentials.

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In this work, we obtained an approximate bound state solution to Schrodinger with Hulthen plus exponential Coulombic potential with centrifugal potential barrier using parametric Nikiforov-Uvarov method. We obtained both the eigen energy and the wave functions to non -relativistic wave equations. We implement Matlab algorithm to obtained the numerical bound state energies for various values of adjustable screening parameter at various quantum state.. The developed potential reduces to Hulthen potential and the numerical bound state energy conform to that of existing literature. KEYWORDSSchrodinger equation Hulthen plus exponential Coulombic potential, Nikiforov-Uvarov method.

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